THE SIGNIFICANCE OF OPTIMAL ALGORITHMS FOR FRACTIONAL-ORDER DIFFERENTIAL EQUATIONS IN MODELING DYNAMIC PROCESSES IN THE FINANCIAL MARKET

Modern financial markets exhibit complex, non-linear behaviors that classical integer-order models often fail to capture adequately. The application of fractional- order differential equations (FODEs) has emerged as a superior mathematical framework due to its inherent ability to model "memory effects" and long-range dependencies in asset price fluctuations. This research focuses on the critical role of optimal algorithms in solving these equations to enhance the predictive accuracy of financial models.